How would I make a Cube look like a text box?
I am by no means a good modeler, but this is how I would do it. 


Start with a plane in top view (NUM 7)
Scale on X so its a rectangle.
CTRL R in edit view to add edge loops, Slide them over how I did in video.
Pull down middle vertex to add the tail. 
Select all 4 corner vertices and hit CNTRL + Shift + B for vertex bevel, slide up on mouse wheel for smoother corner. 
Select all in edit mode and then hit E to extrude. 




I am sure someone can find a quick and cleaner solution but this is my best effort. 

EDIT:

Added in how I would do it with curves (Thanks to Cegaton comment)


Start by adding a 2D Curve object (Rectangle) in top view (NUM 7)
Scale on X so its a rectangle.
Select the bottom two corners in edit mode and hit W to subdive, CTRLR to duplicate a couple times. 
Grab the curve vertices where you want the tail to be.  
You will have to play with the handles in edit mode to get the desired look. 
Go to your curve editor and change the extrude and bevel to taste.